Question 43
Let circles $\Gamma_{1}$ and $\Gamma_{2}$, with centers $O_{1}$ and $O_{2}$ respectively, intersect in two distinct points $A$ and $B$. The line $O_{1} A$ intersects $\Gamma_{2}$ again in $C$ and the line $O_{2} A$ intersects $\Gamma_{1}$ again in $D$. The line through $B$ parallel to $A D$ intersects $\Gamma_{1}$ again in $E$. Assume that $O_{1} A$ is parallel to $D E$. Prove that $C D$ is perpendicular to $O_{2} C$.